Do I need to apply a mirror modifier before exporting to Unity?
In exporting options, you may see that in many cases there is Apply modifiers option, and often it is ticked by default:

Example is for .ply, the same behaviour is in case of exporting to .fbx, .obj, .x3d. Note: default options of Blender itself also may be changed. 
In this case your exported objects/s will be actually mirrored without your action.
With that option unticked you will notice difference because if not applied, modifiers change how the object is displayed and rendered, but not actual geometry.